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Vertex Fault-Tolerant Emulators

Authors Greg Bodwin, Michael Dinitz, Yasamin Nazari

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ACM Subject Classification
  • Theory of computation → Sparsification and spanners
Keywords
  • Emulators
  • Fault Tolerance
  • Girth Conjecture

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Abstract

A k-spanner of a graph G is a sparse subgraph that preserves its shortest path distances up to a multiplicative stretch factor of k, and a k-emulator is similar but not required to be a subgraph of G. A classic theorem by Althöfer et al. [Disc. Comp. Geom. '93] and Thorup and Zwick [JACM '05] shows that, despite the extra flexibility available to emulators, the size/stretch tradeoffs for spanners and emulators are equivalent. Our main result is that this equivalence in tradeoffs no longer holds in the commonly-studied setting of graphs with vertex failures. That is: we introduce a natural definition of vertex fault-tolerant emulators, and then we show a three-way tradeoff between size, stretch, and fault-tolerance for these emulators that polynomially surpasses the tradeoff known to be optimal for spanners.
We complement our emulator upper bound with a lower bound construction that is essentially tight (within log n factors of the upper bound) when the stretch is 2k-1 and k is either a fixed odd integer or 2. We also show constructions of fault-tolerant emulators with additive error, demonstrating that these also enjoy significantly improved tradeoffs over those available for fault-tolerant additive spanners.

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Greg Bodwin, Michael Dinitz, and Yasamin Nazari. Vertex Fault-Tolerant Emulators. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 25:1-25:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022) https://doi.org/10.4230/LIPIcs.ITCS.2022.25

Author Details

Greg Bodwin
  • University of Michigan, Ann Arbor, MI, USA
Michael Dinitz
  • Johns Hopkins University, Baltimore, MD, United States
Yasamin Nazari
  • University of Salzburg, Austria

Funding

  • Dinitz, Michael: Supported in part by NSF award CCF-1909111.
  • Nazari, Yasamin: Supported in part by NSF award CCF-1909111 and by Austrian Science Fund (FWF) grant P 32863-N.

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